I find 'feeling X nationality' when its quite distant and you haven't lived there a bit odd. But dont judge people for it.
My mum was Irish. Her mum was, her dad was Greek and met my nana in england. I spent my first years in Ireland as mum moved back.
My dad is another ethnicity all together and i am mixed race. We don't have much to do with dad's side. I don't really feel half South Asian because it hasnt influenced my life so much.
When mum moved back to England most of my time was spent with my Irish family that lived here and definitely has (as I have got older) impacted my view of things and who I am.
I dont consider myself Irish or English. I dont really celebrate either. Though we do have a few Irish traditions. I certainly dont feel greek because my grandad was though, he did influence my life alot as well.
My nationality and heritage is something I really think about only when answering the question on forms.
To be honest, I think alot of people cling on to their long Irish ancestors, because there's a view that being English is a bit shit. Mainly online. Lots of Americans certainly do this.
Yesterday my family exchanged Happy St Patrick day messages. That was about it.